His proof works, just replace the first two statements to \(4k+3k=-\frac{b}{a}\) and \(4k*3k=\frac{c}{a}\) and do the exact same steps: \(k=-\frac{b}{7a}\). Plug in:\(12*(-\frac{b}{7a})^2=\frac{c}{a}\), which simplifies to \(12b^2=49ac\).